Face FixerFace FixerCompressing Polygon MeshesCompressing Polygon Meshes

with Propertieswith Properties

Martin Isenburg Jack SnoeyinkMartin Isenburg Jack Snoeyink

University of North Carolina at Chapel HillUniversity of North Carolina at Chapel Hill

Polygon Models: Triceratops

356356 trianglestriangles22662266 quadranglesquadrangles

140140 pentagonspentagons6363 hexagonshexagons1010 heptagonsheptagons

77 octagonsoctagons22 undecagonsundecagons

Polygon Models: Others

Faces and Corners: Sandal

• Fewer polygonsFewer polygons less connectivity information less connectivity information

• Polygons tend to be planar & convexPolygons tend to be planar & convex better geometry prediction better geometry prediction

• Better triangle stripsBetter triangle strips

Do not triangulate!

Group Structures: Teapot & Cow

Group Structures: Others

Overview

• Do not triangulate!Do not triangulate!

• Connectivity Compression for Manifold Connectivity Compression for Manifold Polygon MeshesPolygon Meshes• Compact mesh representations

• Simple implementation

• Beyond Faces: Quadrilateral grids

• Capture Structures!Capture Structures!

Previous WorkPrevious Work

Previous Work

• Fast RenderingFast Rendering

• Progressive TransmissionProgressive Transmission

• Maximum CompressionMaximum Compression

Previous Work

• Fast RenderingFast Rendering

• Progressive Transmission

• Maximum Compression

graphics boardmain memory

Previous Work

• Fast RenderingFast Rendering

• Progressive Transmission

• Maximum Compression

• Triangle Strips [?]

• Generalized Triangle Mesh [Deering]

• Transparent Vertex Caching [Hoppe,nVIDIA]

Previous Work

• Fast Rendering

• Progressive TransmissionProgressive Transmission

• Maximum CompressionMaximum Compression

main memorystorage / network

Previous Work

• Fast Rendering

• Progressive TransmissionProgressive Transmission

• Maximum Compression

• Progressive Meshes [Hoppe]

• Progressive Forest Split [Taubin et]

• Compressed Progressive Meshes [Pajarola et]

• Progressive Geometry Compression [Khodakovsky et]

Previous Work

• Fast Rendering

• Progressive Transmission

• Maximum CompressionMaximum Compression

• Topological Surgery [Taubin, Rossignac]

• Triangle Mesh Compression [Costa, Gotsman]

• Edgebreaker [Rossignac, King et]

• Cut-border Machine [Gumhold, Strasser]

ver1 (x,y,z)ver2 (x,y,z)ver3 (x,y,z)

vern

Standard Mesh Representation

face1 1 2 3 4face2 3 4 3face3 5 2 1 3

facem

connectivity

n = 10,000 66 KB 60 KBn = 100,000 830 KB 600 KB

n = 1,000,000 10 MB 6 MB

geometry

ver1 (x,y,z)ver2 (x,y,z)ver3 (x,y,z)

vern

Standard Mesh Representation

face1 1 2 3 4face2 3 4 3face3 5 2 1 3

facem

nor1 (x,y,z)nor2 (x,y,z)nor3 (x,y,z)

nori

tex1 (u,v)tex2 (u,v)tex3 (u,v)

texk

col1 (r,g,b)col2 (r,g,b)col3 (r,g,b)

colj

Face FixerFace Fixer

Face Fixer

• encoding is a sequence of labels:encoding is a sequence of labels:• one label . . . . per face

• one label per hole

• one label per handle

• labels and fix it all together

• number of labels = number of edgesnumber of labels = number of edges

• reverse decodingreverse decoding

Face Fixer

F4 F5

R

F3

L S E

Hn

M

Encoding

Encoding

F4

Encoding

F4

F3

Encoding

F4

F3

R

Encoding

F4

F3F5

R

Encoding

F4

F3F5

R

F5

Encoding

F4

F3F5

R

F5

R

Encoding

F4

F3F5

R

F5

R R

Compressing

• Resulting label sequence:Resulting label sequence:

• non-uniform label frequencies

• correlation among subsequent labels

• Adaptive order-3 arithmetic codingAdaptive order-3 arithmetic coding• Compact probability tables

• Fast bit-operations

F4 F3 F5R F5 R F4. . . R RF4 R . . .

Decoding

R

Decoding

R

Decoding

F5

Decoding

F5

Decoding

R

Decoding

F3

Decoding

F4

Decoding

+2.0 +2.0

TG

2.2

2.4

Compression Results

Triceratops 2.1Galleon 2.6Cessna 2.8

Beethoven 2.9Shark 1.7Cupie 2.3

bitsvertexmodel

fragmented disks

half-diskdisk

Non-Manifold Meshes (1)

Non-Manifold Meshes (2)

cutcut

Beyond FacesBeyond Faces

Extension: Quadrilateral Grids

Encoding a Quad Grid

right

left

height

Encoding a Quad Grid

QG

Triceratops 1.9 -0.2Galleon 2.2 -0.4

Beethoven 2.6 -0.3Shark 1.4 -0.3Teapot 1.1 -0.6

Trumpet 0.6 -0.5

bitsvertexmodel

Compression with Quad Grids

diff

Extension: Repeated Patches

StructuresStructures

Extension: Structures

case D

case Bcase A

case C

Super Faces

connected by anedge

connected by avertex

Encoding a Super Face

Encoding a Super Face

Encoding a Super Face

SF

Encoding a Super Face

Encoding a Super Face

F4

Encoding a Super Face

F4

F3

Encoding a Super Face

F4

F3

R

Encoding a Super Face

F4

F3

R

F5

Encoding a Super Face

F4

F3

R

F5 R

Encoding a Super Face

F4

F3

R

F5 R

R

Encoding a Super Face

F4

F3

R

F5 R

RF3

Encoding a Super Face

F4

F3

R

F5 R

RF3

R

+0.1+0.1+0.2+0.1+0.0+0.1

Compression with Structures

bitsvertexmodel diff

Triceratops 2.4 +0.3Galleon 2.7 +0.1Cessna 3.5 +0.7

Beethoven 3.0 +0.1Shark 2.0 +0.3Cupie 2.3 +0.1

SummarySummary

Summary of Contributions

• Compress polygonal connectivityCompress polygonal connectivity• simpler, more compact, extensions

• Capture structural informationCapture structural information• face groupings

• mesh partitions

• discontinuity curves

• Model LibrariesModel Libraries• “rich” meshes

• storage / network transmission

Current and Future Work

• Triangle Strip CompressionTriangle Strip Compression Graphics Interface 2000Graphics Interface 2000

• Tetrahedral and Hexahedral meshes Tetrahedral and Hexahedral meshes “cell fixer”“cell fixer”

Acknowledgements

Davis KingDavis King

Jarek RossignacJarek Rossignac

Mike ManiscalcoMike Maniscalco

Stefan GumholdStefan Gumhold

SS66

Viewpoint DatalabsViewpoint Datalabs

Thank you.Thank you.

Regular Irregular Connectivity

• Re-meshableRe-meshable• Bunnies, Horses, various Roman Statues, …

• Highly detailed, dense, scanned data sets

• Not Re-meshableNot Re-meshable• Cessnas, Spanish Galleons, Sandals, …

• Careful designed meshes with sharp features

• CAD models, Viewpoint models

Predictive Coding

good not convex bad not planar bad

Attaching Geometry